7.3.5 problem 5

Internal problem ID [45]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.4 (separable equations). Problems at page 43
Problem number : 5
Date solved : Friday, February 07, 2025 at 08:12:54 AM
CAS classification : [_separable]

\begin{align*} 2 \sqrt {x}\, y^{\prime }&=\sqrt {1-y^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 12

dsolve(2*sqrt(x)*diff(y(x),x)=sqrt(1-y(x)^2),y(x), singsol=all)
 

\[ y = \sin \left (\sqrt {x}+\frac {c_1}{2}\right ) \]

✓ Solution by Mathematica

Time used: 0.180 (sec). Leaf size: 32

DSolve[2*Sqrt[x]*D[y[x],x]==Sqrt[1-y[x]^2],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \sin \left (\sqrt {x}+c_1\right ) \\ y(x)\to -1 \\ y(x)\to 1 \\ y(x)\to \text {Interval}[\{-1,1\}] \\ \end{align*}